The study is designed to: 1) determine the force systems delivered from orthodontic appliances and configurations; 2) to develop a mathematical model which has the capacity of predicting orthodontic force systems; and 3) to develop computer techniques that can optimize appliance design. Force systems will be determined by two methods: 1) the analytical, and 2) the experimental. The analytical technique is based on beam theory that is capable of handling large deflections in three dimensions. The experimental component of the project will use a specially designed: 1) force transducer to measure forces and moments in three dimensions; 2) and a stereometric system to accurately determine wire-attachment geometry. On the basis of the experimental data, a predictive mathematical model will be refined to allow the development of computer simulation techniques capable of optimizing appliance design for clinical and research applications.